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Twisted Yang-Baxter sets, cohomology theory, and application to knots
Published 3 Jan 2024 in math.GT and math.QA | (2401.01533v2)
Abstract: We introduce twisted set-theoretic Yang-Baxter solutions and develop an associated cohomology theory, which extends the standard cohomology theory of Yang-Baxter solutions. By employing cocycles of twisted biquandles along with Alexander numbering, we construct state-sum invariants for knots and knotted surfaces. As an application, we use our approach to distinguish the $2$-twist spun trefoil from its reverse orientation, in line with prior findings.
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